Tajarrod, M., Sistani, T. (2018). Spectra of some new extended corona. Algebraic Structures and Their Applications, 5(2), 23-34. doi: 10.29252/asta.5.2.23

Maliheh Tajarrod; Tahereh Sistani. "Spectra of some new extended corona". Algebraic Structures and Their Applications, 5, 2, 2018, 23-34. doi: 10.29252/asta.5.2.23

Tajarrod, M., Sistani, T. (2018). 'Spectra of some new extended corona', Algebraic Structures and Their Applications, 5(2), pp. 23-34. doi: 10.29252/asta.5.2.23

Tajarrod, M., Sistani, T. Spectra of some new extended corona. Algebraic Structures and Their Applications, 2018; 5(2): 23-34. doi: 10.29252/asta.5.2.23

^{}Department of Mathematics, Kerman Branch, Islamic Azad University, Kerman, Iran

Abstract

For two graphs $\mathrm{G}$ and $\mathrm{H}$ with $n$ and $m$ vertices, the corona $\mathrm{G}\circ\mathrm{H}$ of $\mathrm{G}$ and $\mathrm{H}$ is the graph obtained by taking one copy of $\mathrm{G}$ and $n$ copies of $\mathrm{H}$ and then joining the $i^{th}$ vertex of $\mathrm{G}$ to every vertex in the $i^{th}$ copy of $\mathrm{H}$. The neighborhood corona $\mathrm{G}\star\mathrm{H}$ of $\mathrm{G}$ and $\mathrm{H}$ is the graph obtained by taking one copy of $\mathrm{G}$ and $n$ copies of $\mathrm{H}$ and joining every neighbor of the $i^{th}$ vertex of $\mathrm{G}$ to every vertex in the $i^{th}$ copy of $\mathrm{H}$. In this paper, we define four new extensions of corona and neighborhood corona of two graphs $\mathrm{G}$ and $\mathrm{H}$; named the identity-extended corona, identity-extended neighborhood corona, neighborhood extended corona and neighborhood extended neighborhood corona and then determine the spectrum of their adjacency matrix, where $\mathrm{H}$ is a regular graph. As an application, we exhibit infinite families of integral graphs.

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